The emerging K2NiF4-type oxyhydrides with unique hydride ions (H−) and O2- coexisting in the anion sublattice offer superior functionalities for numerous applications. However, the exploration and innovations of the oxyhydrides are challenged by their rarity as a limited number of compounds reported in experiments, owing to the stringent laboratory conditions. Herein, we employed a suite of computations involving ab initio methods, informatics and machine learning to investigate the stability relationship of the K2NiF4-type oxyhydrides. The comprehensive stability map of the oxyhydrides chemical space was constructed to identify 76 new compounds with good thermodynamic stabilities using the high-throughput computations. Based on the established database, we reveal geometric constraints and electronegativities of cationic elements as significant factors governing the oxyhydrides stabilities via informatics tools. Besides fixed stoichiometry compounds, mixed-cation oxyhydrides can provide promising properties due to the enhancement of compositional tunability. However, the exploration of the mixed compounds is hindered by their huge quantity and the rarity of stable oxyhydrides. Therefore, we propose a two-step machine learning workflow consisting of a simple transfer learning to discover 114 formable oxyhydrides from thousands of unknown mixed compositions. The predicted high H− conductivities of the representative oxyhydrides indicate their suitability as energy conversion materials. Our study provides an insight into the oxyhydrides chemistry which is applicable to other mixed-anion systems, and demonstrates an efficient computational paradigm for other materials design applications, which are challenged by the unavailable and highly unbalanced materials database.